CN109738093B - On-chip resonant beam structure for detecting stress of micro-electromechanical device and detection method - Google Patents
On-chip resonant beam structure for detecting stress of micro-electromechanical device and detection method Download PDFInfo
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Abstract
The invention relates to an on-chip resonance beam structure for detecting the stress of a micro-electromechanical device and a detection method, wherein the on-chip resonance beam structure comprises the micro-electromechanical device and a resonance beam; the micro-electro-mechanical device comprises a structural layer, an anchor point layer and a substrate layer which are sequentially arranged from top to bottom; the resonance beam is of a U-shaped structure and is arranged between the structural layer and the substrate layer, and two ends of the top and the bottom of the U-shaped structure are fixed on the substrate layer through 3 anchor points; a detection electrode is arranged in the U-shaped structure of the resonant beam, and the end part of the detection electrode is fixedly connected with the substrate layer through an anchor point; the upper side and the lower side of the exterior of the U-shaped structure of the resonant beam are respectively provided with an external detection electrode, and the two external detection electrodes are fixedly connected with the substrate layer through anchor points; a capacitor is arranged between the resonance beam and the inner and outer detection electrodes, voltage is applied between the resonance beam and the detection electrodes to generate electrostatic force to drive the resonance beam to vibrate, and the vibration of the resonance beam is detected through the change of the capacitance between the detection electrodes and the resonance beam. The invention can be widely applied to the field of stress detection of micro-electromechanical devices.
Description
Technical Field
The invention belongs to the technical field of micro-electromechanical sensors, actuators and micro-electromechanical systems, and particularly relates to an on-chip resonant beam structure for stress detection of micro-electromechanical devices and a detection method.
Background
Stress in the structure of a microelectromechanical device is often an important factor affecting the performance of the device. Some sensors rely on the stress effect to perform the sensitivity to physical quantities themselves, such as accelerometers relying on the stress-resistance conversion effect and microelectromechanical microphones relying on the piezoelectric effect. Structural stresses in these cases can directly lead to undesirable sensor output. In other sensors and actuators, changes in structural stress can cause changes in device structure geometry. For example, in a capacitive accelerometer using closed loop control of force balance, if the position of the proof mass is shifted by stress, the control circuit will generate a voltage to correct the shift, thereby causing a change in the zero offset of the accelerometer. In the micro-electromechanical angular rate gyroscope, when the position of the sensitive mass block is deviated, the supporting rigidity of the structure in all directions is changed, and the coupling signal and the zero offset of the gyroscope are changed accordingly.
The primary factor that causes structural stress to vary is often temperature. Different materials, such as silicon and glass, have unequal coefficients of thermal expansion, so that the stresses within the structure change as the temperature changes between the different materials bonded together. And the thermal expansion coefficient of the material also changes along with the temperature, so that the thermal stress and the temperature are not in a simple linear relation. The output of the mems will also tend to exhibit a non-linear relationship with temperature.
The existing stress test methods are listed below:
1) the surface processing test structure takes electroplated gold as a structural layer, designs a stress test structure taking uplift and rotation as an indication principle, and measures the deformation of the structure by using an optical topography instrument.
2) And designing a beam structure, and measuring the resonance frequency of the beam by using a scanning laser Doppler vibrometer to obtain the residual stress parameters.
3) The beam and the contact detection electrode with two fixed ends are designed, and the stress can cause the beam to generate transverse displacement, so that the beam is contacted with the adjacent electrode to conduct electricity, and the deformation and the stress are judged.
4) And measuring the residual stress of the polysilicon MEMS device by Raman spectroscopy.
5) In the aspect of packaging of the device, the packaging stress of the structure is tested by using piezoresistive effect.
However, in the above methods, the method of measuring stress by an optical instrument is limited by the packaging condition of the device, and generally, optical measurement cannot be performed after the microstructure is packaged. Stress is measured by a method of electrode contact caused by structural deformation, generally, only a limited number of electrodes can be arranged, only the approximate range of the stress can be reflected, and the measurement precision is poor. The piezoresistive effect has poor temperature characteristics, and the stress measurement result is greatly influenced by the temperature.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide an on-chip resonant beam structure and a detection method for detecting stress of a micro-electromechanical device, in which a resonant beam is used as a stress detection element, and structural stress is detected by testing a natural frequency of the resonant beam.
In order to achieve the purpose, the invention adopts the following technical scheme: an on-chip resonance beam structure for stress detection of a micro-electromechanical device comprises the micro-electromechanical device and a resonance beam arranged on the micro-electromechanical device; the micro-electro-mechanical device comprises a structural layer, an anchor point layer and a substrate layer which are sequentially arranged from top to bottom; the resonance beam is of a U-shaped structure, is arranged on the structural layer and is fixed on the substrate layer through two end points at the opening of the U-shaped structure and the end point at the U-shaped bending part respectively through 1 anchor point; an internal detection electrode is arranged in the U-shaped structure, and the end part of the internal detection electrode is fixedly connected with the substrate layer through an anchor point; the upper side and the lower side of the outer part of the U-shaped structure are respectively provided with an external detection electrode, and the two external detection electrodes are fixedly connected with the substrate layer through anchor points; and a capacitor is formed between the U-shaped structure and the internal detection electrode and between the U-shaped structure and the external detection electrode, voltage is applied between the resonance beam and the internal detection electrode and between the resonance beam and the external detection electrode to generate electrostatic force, the resonance beam is driven to vibrate, and the vibration of the resonance beam is detected by detecting the change of the capacitance between the internal detection electrode and the resonance beam and between the internal detection electrode and the external detection electrode and the resonance beam.
Further, the inner detection electrode and the outer detection electrode are flat or comb-shaped electrodes.
Furthermore, the structural layer of the micro-electromechanical device is a conductor and adopts silicon material; the substrate layer is made of glass or silicon material; the anchor point layer is made of silicon, silicon oxide or metal materials.
A stress detection method of an on-chip resonant beam structure for stress detection of a micro-electromechanical device comprises the following steps: 1) arranging a resonance beam structure and a detection electrode on a micro-electromechanical device to be detected, and applying voltage between the resonance beam structure and the detection electrode; 2) and when the temperature changes, detecting the natural frequency and the change of the natural frequency of the resonance beam to obtain a change curve of the stress of the resonance beam along with the temperature.
Further, in the step 2), when the temperature changes,the method for detecting the natural frequency and the change thereof of the resonance beam to obtain the change curve of the stress of the resonance beam along with the temperature comprises the following steps: 2.1) when the resonance beam is not stressed axially, obtaining the first-order natural frequency f of the resonance beam according to the material and the structural size of the resonance beam0(ii) a 2.2) when the resonance beam is subjected to the axial force N, calculating to obtain the first-order natural frequency f of the resonance beam0Relation to axial force N; 2.3) according to the first order natural frequency f of the resonant beam when the temperature changes0And obtaining a change curve of the axial force, namely stress, applied to the resonant beam along with the temperature according to the relation with the axial force N.
Further, in the step 2.1), the first-order natural frequency f of the resonance beam0Comprises the following steps:
wherein E is the elastic modulus of the resonance beam, I is the inertia moment of the section of the resonance beam when the resonance beam is subjected to bending deformation, rho is the density of the resonance beam, A is the sectional area, l is the beam length of the resonance beam, and a is approximately equal to 4.73.
Further, in the step 2.2), the first-order natural frequency f of the resonance beam0The relationship with the axial force N is:
wherein c is approximately equal to 0.0245775 and has no dimension.
Further, in the step 2.3), a change curve of the axial force, i.e., stress, received by the resonant beam with temperature is as follows:
N≈ESiASi(αG-αSi)△T，
wherein E isSiIs the modulus of elasticity of silicon, ASiIs the equivalent cross-sectional area of the silicon beam, αSiAnd αGThermal expansion coefficients of silicon and glass, △ T ═ T-T0，T0Is the unstressed temperature, and T is the temperature.
Due to the adoption of the technical scheme, the invention has the following advantages: 1) the structure of the micro-electromechanical device is provided with the resonant beam structure, the detection electrodes are arranged inside and outside the resonant beam structure and are fixedly connected with the substrate layer through the anchor point layer on the micro-electromechanical device, the stress test is not restricted by the packaging condition of the micro-electromechanical device, and the application range is wide; 2) the stress test of the resonance beam can be carried out in real time under the actual working condition (such as temperature condition) of the micro-electromechanical device, and the optical test method is difficult to use under the condition; 3) the invention only needs to use a simpler driving circuit and a simpler capacitance detection circuit, is matched with a signal analysis card, does not need expensive instruments and equipment such as an optical topographer, a laser Doppler vibrometer, a Raman spectrometer and the like, and has low detection cost and high test efficiency. Therefore, the invention can be widely applied to the field of stress detection of the micro-electromechanical device.
Drawings
FIG. 1 is a cross-sectional view of a micro-electromechanical device structure;
FIG. 2 is a schematic diagram of a stress test structure of the present invention;
FIG. 3 is the resonant beam mode of vibration (1 st order) of the present invention;
FIG. 4 is the resonant beam mode of vibration (2 nd order) of the present invention;
FIG. 5 is a resonant beam mode of vibration (3 rd order) of the present invention;
FIG. 6 is the resonant beam mode of vibration of the present invention (4 th order);
FIG. 7 is a graph of a temperature-stress simulation of the present invention;
fig. 8 is a graph of temperature-frequency simulation of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
As shown in fig. 1 and fig. 2, the present invention provides an on-chip resonant beam structure for stress detection of a micro-electromechanical device, which includes a micro-electromechanical device 1 and a resonant beam 2 disposed on the micro-electromechanical device 1. The micro-electromechanical device 1 comprises a structural layer 11, an anchor point layer 12 and a substrate layer 13 which are sequentially arranged from top to bottom. The resonant beam 2 is of a U-shaped structure, is arranged on the structural layer 11, and is fixed to the substrate layer 13 of the micro-electromechanical device 1 through two end points at the opening of the U-shaped structure and three anchor points 21 arranged at the U-shaped bending position. An internal detection electrode 22 is arranged in the U-shaped structure of the resonant beam 2, and the end part of the internal detection electrode 22 is fixedly connected with the substrate layer 13 through an anchor point 23; the upper side and the lower side of the U-shaped structure of the resonant beam 2 are respectively provided with an external detection electrode 24, and the two external detection electrodes 24 are fixedly connected with the substrate layer 13 of the micro-electromechanical device 1 through anchor points 25; a capacitance is formed between the resonance beam 2 and the inner detection electrode 22 and the two outer detection electrodes 24. A voltage is applied between the resonant beam 2 and the internal and external detection electrodes 22, 24 to generate an electrostatic force and drive the resonant beam 2 to vibrate, and the vibration of the resonant beam is detected by detecting a change in capacitance between the resonant beam 2 and the internal and external electrodes 22, 24.
In the above embodiment, the structural layer 11 of the micro-electromechanical device 1 is a conductor, and usually adopts a silicon material; the substrate layer 13 is typically made of glass or silicon material; anchor layer 12 is typically silicon, silicon oxide, or a metal.
In the above embodiment, the inner detection electrode 22 and the outer detection electrode 24 are formed in a flat plate shape or a comb-tooth shape, and the comb-tooth electrode is used in the present invention.
Based on the above on-chip resonant beam structure for stress detection of the micro-electromechanical device, the present invention further provides a stress detection method for an on-chip resonant beam structure for stress detection of the micro-electromechanical device, when temperature changes, the elastic modulus and the structure size of the material of the structure layer and the substrate layer of the micro-electromechanical device change, so that the resonant beam is subjected to axial stress, and thus the natural frequency changes, and the change of the structural stress along with the temperature can be obtained by detecting the natural frequency and the change of the natural frequency of the resonant beam, specifically, the method comprises the following steps:
1) a resonance beam structure and a detection electrode are arranged on a micro-electromechanical device to be detected, and voltage is applied between the resonance beam structure and the detection electrode. The level of the applied voltage is determined according to the structural parameters and the resonant frequency of the resonant beam, and generally, the applied voltage is selected to be several volts.
2) And when the temperature changes, detecting the natural frequency and the change of the natural frequency of the resonance beam to obtain a change curve of the stress of the resonance beam along with the temperature.
Specifically, the method comprises the following steps:
2.1) when the resonance beam is not stressed axially, obtaining the 2 nd order natural frequency f of the resonance beam at normal temperature according to the material and the structural size of the resonance beam0The invention takes the 2 nd order natural frequency of the resonance beam as the working mode.
First order natural frequency f of the resonant beam when the resonant beam is not axially stressed0Comprises the following steps:
wherein E is the elastic modulus of the resonance beam, I is the inertia moment of the section of the resonance beam when the resonance beam is subjected to bending deformation, rho is the density of the resonance beam, A is the sectional area, l is the beam length of the resonance beam, and a is approximately equal to 4.73.
2.2) when the resonance beam is subjected to the axial force N, calculating to obtain the first-order natural frequency f of the resonance beam0Relationship to axial force N:
wherein c is approximately equal to 0.0245775 and has no dimension.
2.3) according to the first order natural frequency f of the resonant beam when the temperature changes0And obtaining a change curve of the axial force, namely stress, applied to the resonant beam along with the temperature according to the relation with the axial force N.
The stress of the resonant beam structure is analyzed by taking silicon as a structural layer and Pyrex glass as a substrate layer as an example. As the temperature changes, the silicon structure changes its dimensions due to thermal expansion, and the elastic modulus changes. The resonant beam will experience axial forces due to the mismatch in the coefficients of thermal expansion of silicon and glass. Assuming uniform distribution of stress in the glass substrate between the bonding points, let the stress-free temperature be T0Definition △ T ═ T-T0At T, since the force and reaction between the silicon beam and the glass substrate are equal0The vicinity is:
wherein lbondAs the actual distance between the bonding points, ESi、EGElastic moduli of silicon and glass, ASi、AGEquivalent cross-sectional areas of the silicon beam and the glass, respectively,/b0Distance between bonding points in the absence of stress, αSiAnd αGThe thermal expansion coefficients of silicon and glass, respectively. When the structural layer and the substrate layer are made of other materials, the corresponding elastic modulus and the thermal expansion coefficient need to be adjusted according to different materials.
The actual distance l between the bonding points can be obtained from equation (3)bondComprises the following steps:
due to ESiAnd EGAre of the same order in magnitude, and AG＞＞ASiTherefore, the following are:
lbond≈lb0(1+αG△T) (5)
according to the formula (5), the actual distance between the bonding points is mainly determined by the thermal expansion coefficient of the glass, and the change of the axial force applied to the resonant beam with the temperature is as follows:
N≈ESiASi(αG-αSi)△T (6)
in a large temperature range, i.e. when the thermal expansion coefficient changes greatly compared with the normal temperature and cannot be regarded as constant, the thermal expansion coefficient should have
Note αd＝αG-αSiThen there is
The invention is further described below by means of specific examples.
1. The vibration mode of the on-chip resonance beam structure (hereinafter referred to as stress test structure) for detecting the stress of the micro-electromechanical device, which is provided by the invention, is analyzed at the temperature of 20 ℃. In this example, the vibration mode of the resonant beam was analyzed with 20 ℃ as normal temperature.
At 20 ℃, the 1 st to 4 th order vibration modes of the resonance beam are shown in fig. 3 to 6, and it can be seen from the figures that the 2 nd order vibration mode is most suitable for stress-frequency conversion to detect the stress of the structure.
The natural frequencies of the 1 st to 4 th order vibration modes of the resonant beam at 20 c are shown in table 1 below.
TABLE 1 Natural frequencies of the modes of each order of the resonant Beam
| Order of |
1 | 2 | 3 | 4 |
| Natural frequency (Hz) | 42644 | 42695 | 65428 | 74748 |
2. And establishing a finite element model for the stress test structure, and performing finite element simulation on the temperature-stress relation.
Establishing a finite element model for the stress test structure, setting the thermal expansion coefficients of the silicon and glass structures, and carrying out simulation analysis on the stress in the resonant beam along the crystal directions of [110] and [100] in the temperature range of-50 to +85 ℃. The simulations assume that the structure is completely free of internal stress at 20 ℃.
The temperature-stress relationship curve is made taking the axial stress at the geometric center of the resonant beam as a representative of the internal stress of the resonant beam, as shown in fig. 7. The stress in the silicon structure along the <110> and <100> crystal directions is shown, respectively.
3. Finite element simulation is carried out on the temperature-frequency relation of the stress test structure.
As shown in fig. 8, the natural frequency of the stress test structure is plotted against temperature. The stress test structure can generate thermal deformation at different temperatures, and thermal stress is generated inside the stress test structure. And simulating the natural frequency of the resonant beam along the crystal directions of [110] and [100] in the temperature range of-50 to +85 ℃ in the stress test structure. The simulation result shows that when the temperature is higher, the axial stress is tensile stress, and when the temperature is lower, the axial stress is compressive stress, and the axial stress in the resonant beam and the temperature present a nonlinear relationship.
The above embodiments are only used for illustrating the present invention, and the structure, connection mode, manufacturing process, etc. of the components may be changed, and all equivalent changes and modifications performed on the basis of the technical solution of the present invention should not be excluded from the protection scope of the present invention.
Claims (8)
1. An on-chip resonance beam structure for stress detection of a micro-electro-mechanical device is characterized in that: the micro-electromechanical device comprises a micro-electromechanical device and a resonance beam arranged on the micro-electromechanical device;
the micro-electro-mechanical device comprises a structural layer, an anchor point layer and a substrate layer which are sequentially arranged from top to bottom;
the resonance beam is of a U-shaped structure, is arranged on the structural layer and is fixed on the substrate layer through two end points at the opening of the U-shaped structure and an end point at the U-shaped bending part respectively through 1 anchor point; an internal detection electrode is arranged in the U-shaped structure, and the end part of the internal detection electrode is fixedly connected with the substrate layer through an anchor point; the upper side and the lower side of the outer part of the U-shaped structure are respectively provided with an external detection electrode, and the two external detection electrodes are fixedly connected with the substrate layer through anchor points; and a capacitor is formed between the U-shaped structure and the internal detection electrode and between the U-shaped structure and the external detection electrode, voltage is applied between the resonance beam and the internal detection electrode and between the resonance beam and the external detection electrode to generate electrostatic force, the resonance beam is driven to vibrate, and the vibration of the resonance beam is detected by detecting the change of the capacitance between the internal detection electrode and the resonance beam and between the internal detection electrode and the external detection electrode and the resonance beam.
2. The on-chip resonant beam structure for stress sensing of microelectromechanical devices as recited in claim 1, wherein: the internal detection electrode and the external detection electrode adopt flat plate-shaped or comb-tooth-shaped electrodes.
3. The on-chip resonant beam structure for stress sensing of microelectromechanical devices as recited in claim 1, wherein: the structure layer of the micro-electro-mechanical device is a conductor and adopts silicon material; the substrate layer is made of glass or silicon material; the anchor point layer is made of silicon, silicon oxide or metal materials.
4. A stress detection method using the on-chip resonant beam structure for stress detection of the microelectromechanical device as set forth in any of claims 1 to 3, characterized by comprising the steps of:
1) arranging a resonance beam structure and a detection electrode on a micro-electromechanical device to be detected, and applying voltage between the resonance beam structure and the detection electrode;
2) and when the temperature changes, detecting the natural frequency and the change of the natural frequency of the resonance beam to obtain a change curve of the stress of the resonance beam along with the temperature.
5. The method of claim 4, wherein the stress detection method comprises: in the step 2), when the temperature changes, the method for detecting the natural frequency and the change of the natural frequency of the resonance beam to obtain the change curve of the stress of the resonance beam along with the temperature comprises the following steps:
2.1) when the resonance beam is not stressed axially, obtaining the first-order natural frequency f of the resonance beam according to the material and the structural size of the resonance beam0；
2.2) when the resonance beam is subjected to the axial force N, calculating to obtain the first-order natural frequency f of the resonance beam0Relation to axial force N;
2.3) according to the first order natural frequency f of the resonant beam when the temperature changes0And obtaining a change curve of the axial force, namely stress, applied to the resonant beam along with the temperature according to the relation with the axial force N.
6. The method of claim 5, wherein the stress sensing comprises: in the step 2.1), the first-order natural frequency f of the resonance beam0Comprises the following steps:
wherein E is the elastic modulus of the resonance beam, I is the inertia moment of the section of the resonance beam when the resonance beam is subjected to bending deformation, rho is the density of the resonance beam, A is the sectional area, l is the beam length of the resonance beam, and a is approximately equal to 4.73.
7. The method of claim 5, wherein the stress sensing comprises: in the step 2.2), the first-order natural frequency f of the resonance beam0The relationship with the axial force N is:
wherein c is approximately equal to 0.0245775 and has no dimension.
8. The method of claim 5, wherein the stress sensing comprises: in the step 2.3), a change curve of the axial force, i.e., stress, applied to the resonance beam along with the temperature is as follows:
N≈ESiASi(αG-αSi)△T，
wherein E isSiIs the modulus of elasticity of silicon, ASiIs the equivalent cross-sectional area of the silicon beam, αSiAnd αGThermal expansion coefficients of silicon and glass, △ T ═ T-T0，T0Is the unstressed temperature, and T is the temperature.
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